The feedback control system shown in Figure DPI 0.9 has the transfer function

Design a PID compensator Gcl (s) and a lead-lag compensator GC2 (s) such that, in each case, the closed-loop system is stable in the presence of a time-delay T = 0.1 s. Discuss the capability of each compensator to insure stability in the presence of an increase in the time-delay uncertainty of up to 0.2 second.

FIGURE DP10.9 Feedback control system with a time-delay.

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60 G(s) (s2 4s 6(s 10) Controller Plant Time delay